Q. 34.7( 3 Votes )
The mean of the following frequency distribution of 200 observations is 332. Find the value of x and y.
Answer :
This is a grouped frequency distribution.
To find x and y, we’ll need to find mean of the following distribution by assumed mean method and equate it to the given mean of the following distribution, 332.
And class size, c = 50.
[∵ (150 – 100) = (200 – 150) = (250 – 200) = … = (550 – 500) = 50]
This given data is in exclusive type.
So, let’s construct a table finding midpoints and stating frequencies.
So now, we have
∑fiui = -130 – 3x
And ∑fi = 146 + x + y = 200
Mean is given by
⇒ 
[given, mean = 332 and using the values from the table]
⇒ 
⇒ 
⇒ 43 × 4 = 130 + 3x
⇒ 172 = 130 + 3x
⇒ 3x = 172 – 130
⇒ 3x = 42
⇒ 
⇒ x = 14 …(i)
Since, there are 200 observations.
⇒ Sum of frequencies = 200 [Sum of frequencies depict total number of observation]
⇒ ∑fi = 200
⇒ 146 + x + y = 200
⇒ x + y = 200 – 146
⇒ x + y = 54 …(ii)
Putting the value of x from equation (i) into equation (ii), we get
x + y = 54
⇒ 14 + y = 54
⇒ y = 54 – 14
⇒ y = 40
Thus, the missing frequencies are x = 14 and y = 40.
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